1. Strong light-matter coupling: coherent parametric interactions in a cavity and free space Strong light-matter coupling: coherent parametric interactions in a cavity and free space V. S. Egorov 1, V. N. Lebedev 1, I. B. Mekhov 1, P. V. Moroshkin 2, I. A. Chekhonin 1, and S. N. Bagayev 3 1 St. Petersburg State University, V.A. Fock Institute of Physics, St. Petersburg, Russia 2 Universite de Fribourg, Fribourg, Switzerland 3 Institute of Laser Physics, Siberian Branch of RAS, Novosibirsk, Russia V. S. Egorov 1, V. N. Lebedev 1, I. B. Mekhov 1, P. V. Moroshkin 2, I. A. Chekhonin 1, and S. N. Bagayev 3 1 St. Petersburg State University, V.A. Fock Institute of Physics, St. Petersburg, Russia 2 Universite de Fribourg, Fribourg, Switzerland 3 Institute of Laser Physics, Siberian Branch of RAS, Novosibirsk, Russia

2. The report is focused on Coherent interaction between an optically dense resonant medium and near-resonant laser light Influence of intrinsic light-matter dynamics on nonlinear parametric processes Role of the dispersion of a strongly coupled light-matter system (polaritons) Peculiarities of the strong-coupling regime in a free-space in contrast to cavity interactions

3. Strong-coupling regime of light-matter interaction Two coupled oscillators: field and polarization of a medium I. Energy exchange is faster than decoherence High coupling coefficient, small relaxation (dynamical effects may be significant) Coherence of both field and matter is important (adiabatic elimination cannot be applied) II. Weak external field Key role of reemission (reaction) field (constant-field approximation does not work) External field does not destroy collective behavior of an atomic ensemble (beyond the framework of a single-atom model, in contrast to Rabi flopping, Mollow-Boyd, and other strong-field effects) Photons and matter excitations are presented by nearly equal contributions (polaritons)

4. Strong-coupling regime has attracted attention in Atomic and molecular optics Solid-state optics Dicke superradiance (oscillatory regime) Cavity QED (up to single atom / photon interactions) Dicke superradiance (oscillatory regime) Cavity QED (up to single atom / photon interactions) Exciton-polaritons in semiconductor microcavities with nanostructures (single and multiple QWs and QDs) - Stimulated scattering - Parametric interactions - Squeezing, entanglement - Bose-Einstein condensation Exciton-polaritons in semiconductor microcavities with nanostructures (single and multiple QWs and QDs) - Stimulated scattering - Parametric interactions - Squeezing, entanglement - Bose-Einstein condensation It is important for quantum information processing with both discrete and continuous variables

5. Interactions in a cavity Splitting of a cavity mode (collective vacuum Rabi oscillations) Spatial spectrum is fixed by a cavity Polariton dispersion in a cavity Quantum beats in a two-level medium

6. “Spectrum condensation” in active systems Pumping Broadband gain medium Narrow-band absorbing medium Spectrum condensation of a multimode dye laser with an intracavity absorbing cell (Ne discharge) Spectrum condensation of a multimode dye laser with an intracavity absorbing cell (Ne discharge) Weak coupling: Saturated absorption line Strong coupling: Bright doublet

7. Strong-coupling regime in a free space Short broadband pulse Under linear interactions, frequency spectrum is entirely determined by the input spectrum No coherent density-dependent features in the output spectrum (in contrast to vacuum Rabi oscillations in a cavity) Spectrum Coherent collective oscillations in temporal evolution Possibility to observe collective features in nonlinear parametric interactions Time Spatial spectrum is NOT fixed by a cavity (continuos)

8. D +1 D -1 p -1 D0D0 Nonlinear interaction: D +2 p +2 Nonlinear pump-probe interaction pump probe Bloch equations: Two intersected pulses: Probe Coupled Maxwell-Bloch system Pump

9. Collective optical ringing in an extended medium frequency: Strong coupling condition:

10. Propagation of a probe pulse in the presence of a pump Coherent density- and coordinate- dependent features under nonlinear parametric interaction

12. Experiments in a Ne discharge (588.2 nm) Resonant atom density is n=10 13 cm -3 Transition from strong-coupling to strong-field regime

13. Conclusions Nonstationary interaction of laser pulses with a dense resonant medium was considered under the strong-coupling regime of light-matter interaction Internal collective light-matter dynamics was shown to significantly affect nonlinear parametric interactions between short laser pulses Efficient parametric processes in the strong coupling regime were proved even for the free-space conditions Contrary to stationary strong-field effects, the density- and coordinate-dependent transmission spectra of the probe manifest the importance of collective oscillations and cannot be obtained in the framework of a single-atom model References S.N. Bagayev, V.S. Egorov, I.B. Mekhov, P.V. Moroshkin, I.A. Chekhonin, E.M. Davliatchine, and E. Kindel, Phys. Rev. A 68, 043812 (2003) V.S. Egorov, V.N. Lebedev, I.B. Mekhov, P.V. Moroshkin, I.A. Chekhonin, and S.N. Bagayev, Phys. Rev. A 69, 033804 (2004)